Is their a way to queue or automate particle bakes?
The bad news is, no.
The good news is, yes!
From the Manual:

Bake All Dynamics
Bake all physics systems in the scene, even those of different types. Useful for baking complex setups involving interactions between different physics types.

So, you can't exactly queue, so if there's a specific order you want them to bake, I don't think that's possible without scripting your own solution.
But you CAN bake all the systems in the whole scene all at once by just clicking Bake All.